The graph shows a linear relationship between the number of months ($x$) and the money saved ($y$), and the slope is positive, indicating a direct increase in savings over time.

Steps to determine the equation:

1. Identify the slope (rate of saving per month):

   • From the graph, after 1 month, the savings increase by $100.
   • This suggests that the slope $m$ (rate of savings per month) is 100.

2. Find the y-intercept:

   • The graph crosses the y-axis at $50, so the y-intercept $b = 50$.

3. Form the equation of the line: Using the slope-intercept form $y = mx + b$:

   • $m = 100$ (slope),
   • $b = 50$ (y-intercept).

Thus, the equation that represents the relationship between $x$ and $y$ is: $y = 100x + 50$

Correct Answer:

B. $y = 100x + 50$

Would you like more details on how to calculate the slope or intercept?

Here are 5 related questions for further exploration:

1. How would the equation change if the y-intercept was $100 instead of $50?
2. What does the slope of 100 tell you in the context of this problem?
3. How do you find the equation of a line given two points on a graph?
4. If the slope was negative, how would that affect the interpretation of the graph?
5. Can you calculate the money saved after 6 months using the equation?

Tip: The slope in linear equations represents the rate of change, so in real-life contexts like this, it shows how fast one variable changes relative to another.